Some years ago, in a café by the road, I noticed some pack on the shelf where there was writen 5X33. I calculated it and noticed that the 6 in the middle of 165 was the sum of 1 and 5. Then I realised that, in most cases, the same aplyed if I multiplied a single digit by a number with two repeated digits (3X66=198, or 5X55=275...)
Later I made a table like the one in this unfinished canvas. The digits from one to nine are represented by areas defined by diferent colors: the rectangle in the yellow line for 2, the triangle in the white line for 1, the other rectangle in brown for 7, and more irregular areas for the other digits. Notice that all the areas have the same line of simetry. The 3 in light green, the 8 in red... The 9 (in black) is a special case because it seems to have two areas: a square in the middle and a big area ocupying the right lower side. The zero is the perpendicular line (not represented) linking the zeros on the left.
Multiplications with bigger numbers also have interesting results: 4X33=1332, or 3X777=2331, etc.
I don´t know if this is new or if it has already been thought of and writen. This is not complicated mathematics, it is quite simple.
Most of all I like the aesthetics of it, and to imagine a whole crazy and irrelevant branch of mathematics deriving from this, with specific sets of operations, rules, theories, and its own paradoxes.
Clik image to enlarge: